A080925 Binomial transform of Jacobsthal gap sequence (A080924).

0, 1, 5, 13, 41, 121, 365, 1093, 3281, 9841, 29525, 88573, 265721, 797161, 2391485, 7174453, 21523361, 64570081, 193710245, 581130733, 1743392201, 5230176601, 15690529805, 47071589413, 141214768241, 423644304721, 1270932914165

Offset: 0

Author

Paul Barry, Feb 26 2003

Keywords

• easy
• nonn
• changed

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (2,3).

Crossrefs

Cf. A080926. Essentially the same as A046717.

Programs

Mathematica

CoefficientList[Series[x (1 + 3 x) / ((1 + x) (1 - 3 x)), {x, 0, 40}], x] (* Vincenzo Librandi, Aug 05 2013 *)

Formula

a(n)=Sum{k=1..n, Binomial(n, 2k-2)2^(2k-2)}

a(n)=(3^n-2*0^n+(-1)^n)/2; G.f.: x(1+3x)/((1+x)(1-3x)); E.g.f.: (exp(3x)-2exp(0)+exp(-x))/2. - Paul Barry, May 19 2003